SOLUTION: I can't figure out what the system x=y-4.2 and 2x-3y=-9 can be solved as.

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Question 133010This question is from textbook Algebra 1
: I can't figure out what the system x=y-4.2 and 2x-3y=-9 can be solved as. This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x=y-4.2 Start with the first equation


10x=10y-42 Multiply both sides by 10 to clear the decimal number


10x-10y=-42 Subtract 10y from both sides




Start with the given system of equations:

system%2810x-10y=-42%2C2x-3y=-9%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

10x-10y=-42 Start with the first equation


-10y=-42-10x Subtract 10x from both sides


-10y=-10x-42 Rearrange the equation


y=%28-10x-42%29%2F%28-10%29 Divide both sides by -10


y=%28%28-10%29%2F%28-10%29%29x%2B%28-42%29%2F%28-10%29 Break up the fraction


y=x%2B21%2F5 Reduce



---------------------

Since y=x%2B21%2F5, we can now replace each y in the second equation with x%2B21%2F5 to solve for x



2x-3highlight%28%28x%2B21%2F5%29%29=-9 Plug in y=x%2B21%2F5 into the first equation. In other words, replace each y with x%2B21%2F5. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



2x%2B%28-3%29%281%29x%2B%28-3%29%2821%2F5%29=-9 Distribute -3 to x%2B21%2F5


2x-3x-63%2F5=-9 Multiply


%285%29%282x-3x-63%2F5%29=%285%29%28-9%29 Multiply both sides by the LCM of 5. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



10x-15x-63=-45 Distribute and multiply the LCM to each side



-5x-63=-45 Combine like terms on the left side


-5x=-45%2B63Add 63 to both sides


-5x=18 Combine like terms on the right side


x=%2818%29%2F%28-5%29 Divide both sides by -5 to isolate x



x=-18%2F5 Reduce





-----------------First Answer------------------------------


So the first part of our answer is: x=-18%2F5









Since we know that x=-18%2F5 we can plug it into the equation y=x%2B21%2F5 (remember we previously solved for y in the first equation).



y=x%2B21%2F5 Start with the equation where y was previously isolated.


y=%28-18%2F5%29%2B21%2F5 Plug in x=-18%2F5


y=-18%2F5%2B21%2F5 Multiply


y=3%2F5 Combine like terms (note: if you need help with fractions, check out this solver)



-----------------Second Answer------------------------------


So the second part of our answer is: y=3%2F5









-----------------Summary------------------------------

So our answers are:

x=-18%2F5 and y=3%2F5

which form the point